Introduction to Digital Manufacturing
Introduction to Digital Manufacturing
Aadharsh Aadhithya - CB.EN.U4AIE20001
Anirudh Edpuganti - CB.EN.U4AIE20005
Madhav Kishor - CB.EN.U4AIE20033
Onteddu Chaitanya Reddy - CB.EN.U4AIE20045
Pillalamarri Akshaya - CB.EN.U4AIE20049
Team-1
Introduction to Digital Manufacturing
Question 1
Bolts are mechanical fastners having a hexagonal head and a cylindrical shaft groovedhelically using a profile named the thread profile. Nuts on the other hand have complimentary helical grooves on their inner surfaces
Slicing
Introduction to Digital Manufacturing
Question 2
Model and slice two gears perfectly meshing with each other as given below.
Slicing
Introduction to Digital Manufacturing
Design a Roly-Poly toy. Strategise the modeling and slicing off a rolly poly toy that can be 3D printed. The team should be able to justify that the final 3D printed toy would behave similarly to to the roly-poly tows available in the market
Question 3
Introduction to Digital Manufacturing
Introduction to Digital Manufacturing
\}
\textit{L}
Introduction to Digital Manufacturing
\}
\textit{L}
\}
\textit{U}
Introduction to Digital Manufacturing
\}
\textit{L}
\}
\textit{U}
z
C_L \rightarrow (0,0,c_l)
C_L
Introduction to Digital Manufacturing
\}
\textit{L}
\}
\textit{U}
z
C_L \rightarrow (0,0,c_l)
C_L
C_U \rightarrow (0,0,h_l+c_u)
h_1
C_U
Introduction to Digital Manufacturing
\}
\textit{L}
\}
\textit{U}
z
C_L \rightarrow (0,0,c_l)
C_L
C_U \rightarrow (0,0,h_l+c_u)
h_1
C_U
C_L , C_U = \frac{\int r dm}{\int dm}
Introduction to Digital Manufacturing
\}
\textit{L}
\}
\textit{U}
z
C_L \rightarrow (0,0,c_l)
C_L
C_U \rightarrow (0,0,h_l+c_u)
h_1
C_U
C_L , C_U = \frac{\int r dm}{\int dm}
Depends on the Geometry and Distribution of mass about these axes
Introduction to Digital Manufacturing
\}
\textit{L}
\}
\textit{U}
z
C_L \rightarrow (0,0,c_l)
C_L
C_U \rightarrow (0,0,h_l+c_u)
h_1
C_U
C_L , C_U = \frac{\int r dm}{\int dm}
Suppose the Body is Symmetric about z axis , then Center of mass has no component perpendicular to z axis
Introduction to Digital Manufacturing
\}
\textit{L}
\}
\textit{U}
z
C_L \rightarrow (0,0,c_l)
C_L
C_U \rightarrow (0,0,h_l+c_u)
h_1
C_U
C_L , C_U = \frac{\int r dm}{\int dm}
Suppose the Body is Symmetric about z axis , then Center of mass has no component perpendicular to z axis
Center of Mass is along z axis (0,0,z)
Introduction to Digital Manufacturing
z
C_L \rightarrow (0,0,c_l)
C_L
C_U \rightarrow (0,0,h_l+c_u)
h_1
C_U
C_L , C_U = \frac{\int r dm}{\int dm}
z
C_L
h_1
C_U
\theta
Introduction to Digital Manufacturing
z
C_L
h_1
C_U
\theta
z = ax^2 + by^2
Let us Focus on the lower part
Let us Focus on the lower part
Suppose the Lower Part is a Paraboloid
Project the Paraboloid onto z-x plane, and we will get the figure shown beside
z = ax^2
Introduction to Digital Manufacturing
z
C
h_1
\theta
C = \frac{M_L C_L + M_U C_U}{M_L + M_U}
Introduction to Digital Manufacturing
z
C
h_1
\theta
C = \frac{M_L C_L + M_U C_U}{M_L + M_U}
B
A(x_0,z_0)
x
z - z_0 = 1\frac{1}{2ax_0}(x-x_0)
F
F
(M_L + M_u)g
Introduction to Digital Manufacturing
z
C
h_1
\theta
C = \frac{M_L C_L + M_U C_U}{M_L + M_U}
B
A(x_0,z_0)
x
z - z_0 = 1\frac{1}{2ax_0}(x-x_0)
F
F
(M_L + M_u)g
z = -\frac{1}{2ax_0} (x) + \frac{1}{2a} + ax_0^2
Introduction to Digital Manufacturing
z
C
h_1
\theta
C = \frac{M_L C_L + M_U C_U}{M_L + M_U}
B
A(x_0,z_0)
x
z - z_0 = 1\frac{1}{2ax_0}(x-x_0)
F
F
(M_L + M_u)g
z = -\frac{1}{2ax_0} (x) + \frac{1}{2a} + ax_0^2
x=0
B ~ (0, \frac{1}{2a}+ax_0^2)
Introduction to Digital Manufacturing
z
C
h_1
\theta
B
A(x_0,z_0)
x
F
F
(M_L + M_u)g
(0, \frac{1}{2a}+ax_0^2)
c>\frac{1}{2a}+ax_0^2
Introduction to Digital Manufacturing
z
C
h_1
\theta
B
A(x_0,z_0)
x
F
F
(M_L + M_u)g
(0, \frac{1}{2a}+ax_0^2)
c>\frac{1}{2a}+ax_0^2
z
C
h_1
\theta
B
A(x_0,z_0)
x
F
F
(M_L + M_u)g
(0, \frac{1}{2a}+ax_0^2)
c<\frac{1}{2a}+ax_0^2
Introduction to Digital Manufacturing
z
C
h_1
\theta
B
A(x_0,z_0)
x
F
F
(M_L + M_u)g
(0, \frac{1}{2a}+ax_0^2)
c<\frac{1}{2a}+ax_0^2
Further, This can be Generalised to any geometry
For the Roly-Poly Toy to be in "Stable-Equlibrium", Its Center of Mass should be as low as possible
Further, For an extensive study, it is possible to model the equilibrium of the toy using second-order differential equations with constant coeffitients
\frac{5R}{8}
\frac{h}{4}
C_z = \frac{M_L C_L + M_U C_U}{M_L+M_U}
C_L = \frac{5R}{8}
C_U = \frac{h}{4}
if \, \, \frac{M_L}{ M_U} = 1
\frac{1}{2} ( \frac{5R}{8} + (\frac{h}{4} + R) ) < R
h < \frac{3R}{2}
(h,r) \rightarrow (15mm,5mm)
Slicing
THANK YOU SIR!
Digital Manufacturing Assignment-2
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